Multicritical and crossover phenomena in surface growth

Abstract

Extended scaling forms are usually required to account for the complex behavior near a multicritical point. We explore their role in understanding kinetic phase transitions described by the Kardar-Parisi-Zhang equation for interface growth. For a surface of dimension d=2, an exponentially slow logarithmic-to-power-law crossover is predicted from a renormalization-group analysis and compared with numerical simulations of a deposition and evaporation model. Derivation of scaling forms associated with the kinetic roughening transition at d>2 is presented.